CN105159094A - Design method of optimal control force of LQG controller of automobile active suspension bracket - Google Patents

Abstract

The invention, which belongs to the technical field of the active suspension bracket, relates to a design method of an optimal control force of an LQG controller of an automobile active suspension bracket. On the basis of a one-quarter vehicle driving vibration model, a ride weighting coefficient optimization design simulink simulation model is constructed by using MATLAB/simulink; and optimization designing is carried out to obtain a ride weighting coefficient and an LQG optimal control force by using pavement unevenness displacement as input excitation, tyre dynamic displacement and suspension dynamic deflection as constraint conditions, and root-mean-square value minimization of vertical vibration acceleration of a vehicle body as a design target. According to examples and simulation verification, with the method, an accurate and reliable LQG optimal control force of the active suspension bracket can be obtained; and a reliable optimal control force design method can be provided for the design and control of the active suspension bracket system. Therefore, the design level and product quality of the active suspension bracket system can be improved; the vehicle riding comfort and driving safety are enhanced; and the product design and testing expenses can be reduced.

Description

The method for designing of vehicle active suspension LQG controller Optimal Control Force

Technical field

The present invention relates to vehicle active suspension, particularly the method for designing of vehicle active suspension LQG controller Optimal Control Force.

Background technology

LQG controls because having very strong applicability, is widely applied in active suspension system, and wherein, the determination of Optimal Control Force is the key of LQG Controller of Active Suspension design.But, known according to institute's inspection information, the domestic and international design for vehicle active suspension LQG controller Optimal Control Force at present, mostly according to the tendency of deviser to suspension property, empirically tentatively determine that LQG controls weighting coefficient, then pass through repeatedly analog simulation, progressively adjust weighting coefficient according to response quautity, until obtain satisfied output response quautity, and then design the Optimal Control Force of LQG Controller of Active Suspension.Although the LQG control utilizing the method to obtain, vehicle can be made to meet the requirement of current driving operating mode, but, designed control non-optimal.Along with the fast development of Vehicle Industry and improving constantly of Vehicle Speed, people have higher requirement to vehicle safety and riding comfort, the method of current LQG Controller of Active Suspension Optimal Control Force design, can not meet the requirement of vehicle development and the design of Active suspension control device.Therefore, a kind of method for designing that is accurate, vehicle active suspension LQG controller Optimal Control Force reliably must be set up, meet the requirement of vehicle development and the design of Active suspension control device, improve design level and the product quality of Vehicle Active Suspension System, improve vehicle riding comfort and security; Meanwhile, reduce product design and testing expenses, shorten the product design cycle.

Summary of the invention

For the defect existed in above-mentioned prior art, technical matters to be solved by this invention is to provide a kind of method for designing that is accurate, vehicle active suspension LQG controller Optimal Control Force reliably, and its design flow diagram as shown in Figure 1; 1/4 vehicle ride illustraton of model as shown in Figure 2.

For solving the problems of the technologies described above, the method for designing of vehicle active suspension LQG controller Optimal Control Force provided by the present invention, is characterized in that adopting following design procedure:

(1) the 1/4 vehicle ride differential equation is set up:

According to vehicle single-wheel unsprung mass m ₁, sprung mass m ₂, suspension stiffness K ₂, tire stiffness K _t, Active suspension control power U to be designed _a; With tire vertical deviation z ₁, vehicle body vertical deviation z ₂for coordinate; With road roughness displacement q for input stimulus; Set up the 1/4 vehicle ride differential equation, that is:

$\left\{\begin{array}{c}{m}_2{\stackrel{\·\·}{z}}_2+K_2(z_2-z_1)-U_a=0\\ m_1{\stackrel{\·\·}{z}}_1+K_2(z_1-z_2)+K_t(z_1-q)+U_a=0\end{array}\right.;$

(2) the state matrix A that LQG controls and gating matrix B is determined:

According to vehicle single-wheel unsprung mass m ₁, sprung mass m ₂, suspension stiffness K ₂, tire stiffness K _t, Vehicle Speed v, and filtering white noise road surface spatial-cut-off frequency n _0c, determine the state matrix A that LQG controls and gating matrix B, be respectively:

$A=\left[\begin{array}{ccccc}0& 0& -K_2/m_2& K_2/m_2& 0\\ 0& 0& K_2/m_1& -(K_2+K_t)/m_1& K_t/m_1\\ 1& 0& 0& 0& 0\\ 0& 1& 0& 0& 0\\ 0& 0& 0& 0& -2{\mathrm{\πvn}}_{0c}\end{array}\right],B=\left[\begin{array}{c}1/m_2\\ -1/m_1\\ 0\\ 0\\ 0\end{array}\right];$

(3) the weighting matrix expression formula that LQG controls is determined:

According to vehicle single-wheel unsprung mass m ₁, sprung mass m ₂, suspension stiffness K ₂, tire stiffness K _t, bump clearance of suspension [f _d], and gravity acceleration g, determine about ride comfort weighting coefficient α ₁, α ₂, α ₃state variable, control variable and state variable and control variable cross-product term weighting matrix expression formula Q (α ₁, α ₂, α ₃), R (α ₁, α ₂, α ₃), N (α ₁, α ₂, α ₃), be respectively:

$Q({\mathrm{\α}}_1,{\mathrm{\α}}_2,{\mathrm{\α}}_3)=\left[\begin{array}{ccccc}0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& q_2+K_2^2/m_2^2& -q_2-K_2^2/m_2^2& 0\\ 0& 0& -q_2-K_2^2/m_2^2& q_1+q_2+K_2^2/m_2^2& -q_1\\ 0& 0& 0& -q_1& q_1\end{array}\right],$

$R({\mathrm{\α}}_1,{\mathrm{\α}}_2,{\mathrm{\α}}_3)=\frac{q_3}{m_2^2},$

$N({\mathrm{\α}}_1,{\mathrm{\α}}_2,{\mathrm{\α}}_3)=\frac{1}{m_2^2}\left[\begin{array}{c}0\\ 0\\ -K_2\\ K_2\\ 0\end{array}\right];$

Wherein, q ₃=1; α ₁for the relative dynamic load weighting coefficient of wheel, α ₂for the relative dynamic deflection weighting coefficient of suspension, α ₃for vehicle body vertical vibration relative acceleration weighting coefficient;

(4) Active suspension LQG control U is determined _aexpression formula:

I step: the initial value choosing ride comfort weighting coefficient, i.e. α ₁=k ₁, α ₂=k ₂, α ₃=k ₃, wherein, k ₁, k ₂, k ₃value be greater than zero and be less than 1 numerical value, and k ₁+ k ₂+ k ₃=1.0;

II step: according to the ride comfort weighting coefficient initial values α chosen in I step ₁=k ₁, α ₂=k ₂, α ₃=k ₃, and the weighting matrix expression formula Q (α determined in step (3) ₁, α ₂, α ₃), R (α ₁, α ₂, α ₃), N (α ₁, α ₂, α ₃), calculate weighting matrices Q (k ₁, k ₂, k ₃), R (k ₁, k ₂, k ₃), N (k ₁, k ₂, k ₃);

III step: according to the state matrix A determined in step (2) and gating matrix B, and the weighting matrices Q (k determined in II step ₁, k ₂, k ₃), R (k ₁, k ₂, k ₃), N (k ₁, k ₂, k ₃), utilize the LQR function in Matlab to calculate the control feedback gain matrix K trying to achieve Active suspension LQG;

IV step: according to the feedback gain matrix K determined in III step, with unsteadiness of wheels speed and displacement z ₁, body vibrations speed and displacement z ₂with pavement displacement q as state variable, determine Active suspension LQG control U _aexpression formula, that is:

$U_a=-K{\left[\begin{array}{ccccc}{\stackrel{\·}{z}}_2& {\stackrel{\·}{z}}_1& z_2& z_1& q\end{array}\right]}^T;$

Wherein, ${\left[\begin{array}{ccccc}{\stackrel{\·}{z}}_2& {\stackrel{\·}{z}}_1& z_2& z_1& q\end{array}\right]}^T$ For matrix $\left[\begin{array}{ccccc}{\stackrel{\·}{z}}_2& {\stackrel{\·}{z}}_1& z_2& z_1& q\end{array}\right]$ Transposed matrix;

(5) optimal design of ride comfort weighting coefficient:

1. ride comfort weighting coefficient optimal design realistic model is built

According to the 1/4 vehicle ride differential equation set up in step (1), and the control U that in step (4), IV step is tried to achieve _a, utilize Matlab/Simulink simulation software, build ride comfort weighting coefficient optimal design Simulink realistic model;

2. ride comfort weighting coefficient optimal design objective function is set up

According to the ride comfort weighting coefficient optimal design Simulink realistic model set up in 1. step, with ride comfort weighting coefficient α ₁, α ₂, α ₃for design variable, using road roughness displacement as input stimulus, vehicle ride situation is emulated, utilize the vehicle body Vertical Acceleration root-mean-square value emulating and obtain set up ride comfort weighting coefficient optimal design objective function J _o(α ₁, α ₂, α ₃), that is:

$J_o({\mathrm{\α}}_1,{\mathrm{\α}}_2,{\mathrm{\α}}_3)={\mathrm{\σ}}_{{\stackrel{\·\·}{z}}_2};$

3. ride comfort weighting coefficient Constrained Conditions in Optimal Design is set up

According to vehicle single-wheel unsprung mass m ₁, sprung mass m ₂, tire stiffness K _t, gravity acceleration g, and bump clearance of suspension [f _d], utilize tire vertical deviation z ₁, vehicle body vertical deviation z ₂, road roughness displacement q, and ride comfort weighting coefficient α ₁, α ₂, α ₃, set up ride comfort weighting coefficient Constrained Conditions in Optimal Design, namely

$\left\{\begin{array}{c}\left|z_1-q\right|\≤\frac{(m_1+m_2)g}{K_t}\\ \left|z_2-z_1\right|\≤\[f_d\]\\ 0\≤{\mathrm{\α}}_1\≤1\\ 0\≤{\mathrm{\α}}_2\≤1\\ 0\≤{\mathrm{\α}}_3\≤1\\ {\mathrm{\α}}_1+{\mathrm{\α}}_2+{\mathrm{\α}}_3=1\end{array}\right.;$

4. the optimal design of ride comfort weighting coefficient

According to the ride comfort weighting coefficient optimal design Simulink realistic model set up in 1. step, and the ride comfort weighting coefficient Constrained Conditions in Optimal Design 3. set up in step, with ride comfort weighting coefficient α ₁, α ₂, α ₃for design variable, using road roughness displacement as input stimulus, utilize optimized algorithm ask 2. in step institute set up ride comfort weighting coefficient optimal design objective function J _o(α ₁, α ₂, α ₃) minimum value, corresponding design variable is the optimum optimization design load of ride comfort weighting coefficient, i.e. α _1o, α _2o, α _3o;

(6) LQG Controller of Active Suspension Optimal Control Force U _aodesign:

I step: according to the 4. ride comfort weighting coefficient α that obtains of optimization order design in step (5) _1o, α _2o, α _3o, and the weighting matrix expression formula Q (α determined in step (3) ₁, α ₂, α ₃), R (α ₁, α ₂, α ₃), N (α ₁, α ₂, α ₃), calculate weighting matrices Q (α _1o, α _2o, α _3o), R (α _1o, α _2o, α _3o), N (α _1o, α _2o, α _3o);

Ii step: according to the state matrix A determined in step (2) and gating matrix B, and the weighting matrices Q (α determined in i step _1o, α _2o, α _3o), R (α _1o, α _2o, α _3o), N (α _1o, α _2o, α _3o), utilize the LQR function in Matlab to calculate the optimum control feedback gain matrix K trying to achieve Active suspension LQG _o;

Iii step: according to the Optimal Feedback gain matrix K determined in ii step _o, with unsteadiness of wheels speed and displacement z ₁, body vibrations speed and displacement z ₂with pavement displacement q as state variable, determine the Optimal Control Force U of LQG Controller of Active Suspension _ao, that is:

$U_{ao}=-K_o{\left[\begin{array}{ccccc}{\stackrel{\·}{z}}_2& {\stackrel{\·}{z}}_1& z_2& z_1& q\end{array}\right]}^T.$

The advantage that the present invention has than prior art:

LQG controls because having very strong applicability, is widely applied in active suspension system, and wherein, the determination of Optimal Control Force is the key of LQG Controller of Active Suspension design.But, known according to institute's inspection information, the domestic and international design for vehicle active suspension LQG controller Optimal Control Force at present, mostly according to the tendency of deviser to suspension property, empirically tentatively determine that LQG controls weighting coefficient, then pass through repeatedly analog simulation, progressively adjust weighting coefficient according to response quautity, until obtain satisfied output response quautity, and then design the Optimal Control Force of LQG Controller of Active Suspension.Although the LQG control utilizing the method to obtain, vehicle can be made to meet the requirement of current driving operating mode, but, designed control non-optimal.Along with the fast development of Vehicle Industry and improving constantly of Vehicle Speed, people have higher requirement to vehicle safety and riding comfort, the method of current LQG Controller of Active Suspension Optimal Control Force design, can not meet the requirement of vehicle development and the design of Active suspension control device.

The present invention is according to 1/4 vehicle ride model and Active suspension control power, utilize MATLAB/Simulink, construct ride comfort weighting coefficient optimal design Simulink realistic model, and with road roughness displacement for input stimulus, to take turns movement of the foetus displacement and suspension dynamic deflection for constraint condition, minimum for design object with vehicle body Vertical Acceleration root-mean-square value, optimal design obtains ride comfort weighting coefficient, and then design obtains Active suspension LQG Optimal Control Force.Verify known by design example and simulation comparison, the method can obtain Active suspension LQG optimum control force value accurately and reliably, for the design of vehicle active suspension LQG Optimal Control Force provides reliable method for designing.Utilize the method, not only can improve design level and the product quality of Vehicle Active Suspension System, improve vehicle riding comfort and security; Meanwhile, reduce product design and testing expenses, shorten the product design cycle.

Accompanying drawing explanation

Be described further below in conjunction with accompanying drawing to understand the present invention better.

Fig. 1 is the design flow diagram of vehicle active suspension LQG controller optimum control hydraulic design method;

Fig. 2 is 1/4 vehicle ride illustraton of model;

Fig. 3 is the ride comfort weighting coefficient optimal design Simulink realistic model of embodiment;

Fig. 4 is the simulation comparison curve of the vehicle body Vertical Acceleration time-domain signal of embodiment;

Fig. 5 is the simulation comparison curve of the vehicle body Vertical Acceleration power spectrum density of embodiment.

Specific embodiments

Below by an embodiment, the present invention is described in further detail.

Certain vehicle single-wheel unsprung mass m ₁=40kg, sprung mass m ₂=320kg, suspension stiffness K ₂=20000N/m, tire stiffness K _t=200000N/m, bump clearance of suspension [f _d]=100mm, gravity acceleration g=9.8m/s ², filtering white noise road surface spatial-cut-off frequency n _0c=0.011m ^-1, the LQG control of Active suspension to be designed is U _a.Vehicle Speed v=72km/h required by this Active Suspension Design, designs the control of this LQG Controller of Active Suspension.

The method for designing of the vehicle active suspension LQG controller Optimal Control Force that example of the present invention provides, as shown in Figure 1, as shown in Figure 2, concrete steps are as follows for 1/4 vehicle ride illustraton of model for its design flow diagram:

(1) the 1/4 vehicle ride differential equation is set up:

According to vehicle single-wheel unsprung mass m ₁=40kg, sprung mass m ₂=320kg, suspension stiffness K ₂=20000N/m, tire stiffness K _t=200000N/m, Active suspension control power U to be designed _a; With tire vertical deviation z ₁, vehicle body vertical deviation z ₂for coordinate; With road roughness displacement q for input stimulus; Set up the 1/4 vehicle ride differential equation, that is:

$\left\{\begin{array}{c}{m}_2{\stackrel{\·\·}{z}}_2+K_2(z_2-z_1)-U_a=0\\ m_1{\stackrel{\·\·}{z}}_1+K_2(z_1-z_2)+K_t(z_1-q)+U_a=0\end{array}\right.;$

(2) the state matrix A that LQG controls and gating matrix B is determined:

According to vehicle single-wheel unsprung mass m ₁=40kg, sprung mass m ₂=320kg, suspension stiffness K ₂=20000N/m, tire stiffness K _t=200000N/m, Vehicle Speed v=72km/h, and filtering white noise road surface spatial-cut-off frequency n _0c=0.011m ^-1, determine the state matrix A that LQG controls and gating matrix B, be respectively:

$A=\left[\begin{array}{ccccc}0& 0& -62.5& 62.5& 0\\ 0& 0& 500& -5500& 5000\\ 1& 0& 0& 0& 0\\ 0& 1& 0& 0& 0\\ 0& 0& 0& 0& -1.4\end{array}\right],B=\left[\begin{array}{c}0.0031\\ -0.025\\ 0\\ 0\\ 0\end{array}\right];$

(3) the weighting matrix expression formula that LQG controls is determined:

According to vehicle single-wheel unsprung mass m ₁=40kg, sprung mass m ₂=320kg, suspension stiffness K ₂=20000N/m, tire stiffness K _t=200000N/m, bump clearance of suspension [f _d]=100mm, and gravity acceleration g=9.8m/s ², determine about ride comfort weighting coefficient α ₁, α ₂, α ₃state variable, control variable and state variable and control variable cross-product term weighting matrix expression formula Q (α ₁, α ₂, α ₃), R (α ₁, α ₂, α ₃), N (α ₁, α ₂, α ₃), be respectively:

$Q({\mathrm{\α}}_1,{\mathrm{\α}}_2,{\mathrm{\α}}_3)=\left[\begin{array}{ccccc}0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& q_2+3906.3& -q_2-3906.3& 0\\ 0& 0& -q_2-3906.3& q_1+q_2+3906.3& -q_1\\ 0& 0& 0& -q_1& q_1\end{array}\right],$

$R({\mathrm{\α}}_1,{\mathrm{\α}}_2,{\mathrm{\α}}_3)=\frac{q_3}{102400},$

$N({\mathrm{\α}}_1,{\mathrm{\α}}_2,{\mathrm{\α}}_3)=0.195q_3\left[\begin{array}{c}0\\ 0\\ -1\\ 1\\ 0\end{array}\right];$

Wherein, q ₃=1; α ₁for the relative dynamic load weighting coefficient of wheel, α ₂for the relative dynamic deflection weighting coefficient of suspension, α ₃for vehicle body vertical vibration relative acceleration weighting coefficient;

(4) Active suspension LQG control U is determined _aexpression formula:

I step: the initial value choosing ride comfort weighting coefficient; This embodiment chooses k ₁=0.1, k ₂=0.2, k ₃=0.7, wherein, k ₁+ k ₂+ k ₃=1.0, namely choose the initial value α of ride comfort weighting coefficient ₁=0.1, α ₂=0.2, α ₃=0.7;

II step: according to the ride comfort weighting coefficient initial values α chosen in I step ₁=0.1, α ₂=0.2, α ₃=0.7, and the weighting matrix expression formula Q (α determined in step (3) ₁, α ₂, α ₃), R (α ₁, α ₂, α ₃), N (α ₁, α ₂, α ₃), calculate weighting matrices Q (0.1,0.2,0.7), R (0.1,0.2,0.7), N (0.1,0.2,0.7), that is:

$Q(0.1,0.2,0.7)=\left[\begin{array}{ccccc}0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 4211.1& -4211.1& 0\\ 0& 0& -4211.1& 48302.8& -44091.7\\ 0& 0& 0& -44091.7& 44091.7\end{array}\right],$

R(0.1,0.2,0.7)＝9.766×10 ^-6，

$N(0.1,0.2,0.7)=\left[\begin{array}{c}0\\ 0\\ -0.195\\ 0.195\\ 0\end{array}\right];$

III step: according to the state matrix A determined in step (2) and gating matrix B, and the weighting matrices Q (0.1 determined in II step, 0.2,0.7), R (0.1,0.2,0.7), N (0.1,0.2,0.7), utilize the LQR function in Matlab to calculate and try to achieve Active suspension

The control feedback gain matrix K of LQG, that is:

K＝[1941.2-925.1-14412.513653.011560.0]；

IV step: according to the feedback gain matrix K determined in III step, with unsteadiness of wheels speed and displacement z ₁, body vibrations speed and displacement z ₂with pavement displacement q as state variable, determine Active suspension LQG control U _aexpression formula, that is:

$U_a=-1941.2{\stackrel{\·}{z}}_2+925.1{\stackrel{\·}{z}}_1+14412.51z_2-3653.0z_1-11560.0q;$

Wherein, ${\left[\begin{array}{ccccc}{\stackrel{\·}{z}}_2& {\stackrel{\·}{z}}_1& z_2& z_1& q\end{array}\right]}^T$ For matrix $\left[\begin{array}{ccccc}{\stackrel{\·}{z}}_2& {\stackrel{\·}{z}}_1& z_2& z_1& q\end{array}\right]$ Transposed matrix;

(5) optimal design of ride comfort weighting coefficient:

1. ride comfort weighting coefficient optimal design realistic model is built

According to the 1/4 vehicle ride differential equation set up in step (1), and the control U that in step (4), IV step is tried to achieve _a, utilize Matlab/Simulink simulation software, build ride comfort weighting coefficient optimal design Simulink realistic model, as shown in Figure 3;

2. ride comfort weighting coefficient optimal design objective function is set up

According to the ride comfort weighting coefficient optimal design Simulink realistic model set up in 1. step, with ride comfort weighting coefficient α ₁, α ₂, α ₃for design variable, using road roughness displacement as input stimulus, vehicle ride situation is emulated, utilize the vehicle body Vertical Acceleration root-mean-square value emulating and obtain set up ride comfort weighting coefficient optimal design objective function J _o(α ₁, α ₂, α ₃), that is:

$J_o({\mathrm{\α}}_1,{\mathrm{\α}}_2,{\mathrm{\α}}_3)={\mathrm{\σ}}_{{\stackrel{\·\·}{z}}_2};$

3. ride comfort weighting coefficient Constrained Conditions in Optimal Design is set up

According to vehicle single-wheel unsprung mass m ₁=40kg, sprung mass m ₂=320kg, tire stiffness K _t=200000N/m, gravity acceleration g=9.8m/s ², and bump clearance of suspension [f _d]=100mm, utilizes tire vertical deviation z ₁, vehicle body vertical deviation z ₂, road roughness displacement q, and ride comfort weighting coefficient α ₁, α ₂, α ₃, set up ride comfort weighting coefficient Constrained Conditions in Optimal Design, namely

$\left\{\begin{array}{c}\left|z_1-q\right|\≤18mm\\ \left|z_2-z_1\right|\≤100mm\\ 0\≤{\mathrm{\α}}_1\≤1\\ 0\≤{\mathrm{\α}}_2\≤1\\ 0\≤{\mathrm{\α}}_3\≤1\\ {\mathrm{\α}}_1+{\mathrm{\α}}_2+{\mathrm{\α}}_3=1\end{array}\right.;$

4. the optimal design of ride comfort weighting coefficient

According to the ride comfort weighting coefficient optimal design Simulink realistic model set up in 1. step, and the ride comfort weighting coefficient Constrained Conditions in Optimal Design 3. set up in step, with ride comfort weighting coefficient α ₁, α ₂, α ₃for design variable, using road roughness displacement as input stimulus, utilize optimized algorithm ask 2. in step institute set up ride comfort weighting coefficient optimal design objective function J _o(α ₁, α ₂, α ₃) minimum value, try to achieve the optimum optimization design load of ride comfort weighting coefficient, i.e. α _1o=0.0108, α _2o=0.0506, α _3o=0.9386;

(6) LQG Controller of Active Suspension Optimal Control Force U _aodesign:

I step: according to the 4. ride comfort weighting coefficient α that obtains of optimization order design in step (5) _1o=0.0108, α _2o=0.0506, α _3o=0.9386, and the weighting matrix expression formula Q (α determined in step (3) ₁, α ₂, α ₃), R (α ₁, α ₂, α ₃), N (α ₁, α ₂, α ₃), calculate weighting matrices Q (0.0108,0.0506,0.9386), R (0.0108,0.0506,0.9386), N (0.0108,0.0506,0.9386), that is:

$Q(0.0108,0.0506,0.9386)=\left[\begin{array}{ccccc}0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 3964.2& -3.9642& 0\\ 0& 0& -3.9642& 7515.3& -3551.0\\ 0& 0& 0& -3551.0& 3551.0\end{array}\right],$

R(0.0108,0.0506,0.9386)＝9.766×10 ^-6，

$N(0.0108,0.0506,0.9386)=\left[\begin{array}{c}0\\ 0\\ -0.195\\ 0.195\\ 0\end{array}\right];$

Ii step: according to the state matrix A determined in step (2) and gating matrix B, and the weighting matrices Q (0.0108 determined in i step, 0.0506,0.9386), R (0.0108,0.0506,0.9386), N (0.0108,0.0506,0.9386) the LQR function in Matlab, is utilized to calculate the optimum control feedback gain matrix K trying to achieve Active suspension LQG _o, that is:

K _o＝[1247.4-270.4-1756318032.3347.5]；

Iii step: according to the Optimal Feedback gain matrix K determined in ii step _o, with unsteadiness of wheels speed and displacement z ₁, body vibrations speed and displacement z ₂with pavement displacement q as state variable, determine the Optimal Control Force U of LQG Controller of Active Suspension _ao, that is:

$U_{ao}=-1247.4{\stackrel{\·}{z}}_2+270.4{\stackrel{\·}{z}}_1+17563z_2-18032.3z_1-347.5q.$

Under same vehicle structural parameters and driving cycle, wherein, it is B level road surface that vehicle travels road conditions, Vehicle Speed v=72km/h, respectively to Conventional wisdom method determination Optimal Control Force and utilize the LQG of this Optimization Design Method determination Optimal Control Force control carry out model emulation, wherein, the Optimal Control Force utilizing Conventional wisdom method to determine is $U_a=-711.9{\stackrel{\·}{z}}_2+1241.5{\stackrel{\·}{z}}_1+19284.5z_2+2038.5z_1-20103.2q,$ Emulate the vehicle body Vertical Acceleration time-domain signal of two kinds of control methods and the correlation curve of vehicle body Vertical Acceleration power spectrum density that obtain, respectively as shown in Figure 4, Figure 5, known, the LQG Controller of Active Suspension designed by this Optimization Design Method is utilized to significantly reduce the Vertical Acceleration of vehicle body, compared with Conventional wisdom method for designing, vehicle body Vertical Acceleration root-mean-square value reduces 53.0%, shows that the method for designing of set up vehicle active suspension LQG controller Optimal Control Force is correct.

Claims (1)

1. the method for designing of vehicle active suspension LQG controller Optimal Control Force, its specific design step is as follows:

(1) the 1/4 vehicle ride differential equation is set up:

According to vehicle single-wheel unsprung mass m ₁, sprung mass m ₂, suspension stiffness K ₂, tire stiffness K _t, Active suspension control power U to be designed _a; With tire vertical deviation z ₁, vehicle body vertical deviation z ₂for coordinate; With road roughness displacement q for input stimulus; Set up the 1/4 vehicle ride differential equation, that is:

$\{\begin{array}{c}{m}_2{\stackrel{\·\·}{z}}_2+K_2(z_2-z_1)-U_a=0\\ m_1{\stackrel{\·\·}{z}}_1+K_2(z_1-z_2)+K_t(z_1-q)+U_a=0\end{array};$

(2) the state matrix A that LQG controls and gating matrix B is determined:

According to vehicle single-wheel unsprung mass m ₁, sprung mass m ₂, suspension stiffness K ₂, tire stiffness K _t, Vehicle Speed v, and filtering white noise road surface spatial-cut-off frequency n _0c, determine the state matrix A that LQG controls and gating matrix B, be respectively:

$A=\left[\begin{array}{ccccc}0& 0& -K_2/m_2& K_2/m_2& 0\\ 0& 0& K_2/m_1& -(K_2+K_t)/m_1& K_t/m_1\\ 1& 0& 0& 0& 0\\ 0& 1& 0& 0& 0\\ 0& 0& 0& 0& -2{\mathrm{\πvn}}_{0c}\end{array}\right],B=\left[\begin{array}{c}1/m_2\\ -1/m_1\\ 0\\ 0\\ 0\end{array}\right];$

(3) the weighting matrix expression formula that LQG controls is determined:

According to vehicle single-wheel unsprung mass m ₁, sprung mass m ₂, suspension stiffness K ₂, tire stiffness K _t, bump clearance of suspension [f _d], and gravity acceleration g, determine about ride comfort weighting coefficient α ₁, α ₂, α ₃state variable, control variable and state variable and control variable cross-product term weighting matrix expression formula Q (α ₁, α ₂, α ₃), R (α ₁, α ₂, α ₃), N (α ₁, α ₂, α ₃), be respectively:

$Q({\mathrm{\α}}_1,{\mathrm{\α}}_2,{\mathrm{\α}}_3)=\left[\begin{array}{ccccc}0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& q_2+K_2^2/m_2^2& -q_2-K_2^2/m_2^2& 0\\ 0& 0& -q_2-K_2^2/m_2^2& q_1+q_2+K_2^2/m_2^2& -q_1\\ 0& 0& 0& -q_1& q_1\end{array}\right],$

$R({\mathrm{\α}}_1,{\mathrm{\α}}_2,{\mathrm{\α}}_3)=\frac{q_3}{m_2^2},$

$N({\mathrm{\α}}_1,{\mathrm{\α}}_2,{\mathrm{\α}}_3)=\frac{1}{m_2^2}\left[\begin{array}{c}0\\ 0\\ -K_2\\ K_2\\ 0\end{array}\right];$

Wherein, q ₃=1; α ₁for the relative dynamic load weighting coefficient of wheel, α ₂for the relative dynamic deflection weighting coefficient of suspension, α ₃for vehicle body vertical vibration relative acceleration weighting coefficient;

(4) Active suspension LQG control U is determined _aexpression formula:

I step: the initial value choosing ride comfort weighting coefficient, i.e. α ₁=k ₁, α ₂=k ₂, α ₃=k ₃, wherein, k ₁, k ₂, k ₃value be greater than zero and be less than 1 numerical value, and k ₁+ k ₂+ k ₃=1.0;

II step: according to the ride comfort weighting coefficient initial values α chosen in I step ₁=k ₁, α ₂=k ₂, α ₃=k ₃, and the weighting matrix expression formula Q (α determined in step (3) ₁, α ₂, α ₃), R (α ₁, α ₂, α ₃), N (α ₁, α ₂, α ₃), calculate weighting matrices Q (k ₁, k ₂, k ₃), R (k ₁, k ₂, k ₃), N (k ₁, k ₂, k ₃);

III step: according to the state matrix A determined in step (2) and gating matrix B, and the weighting matrices Q (k determined in II step ₁, k ₂, k ₃), R (k ₁, k ₂, k ₃), N (k ₁, k ₂, k ₃), utilize the LQR function in Matlab to calculate the control feedback gain matrix K trying to achieve Active suspension LQG;

IV step: according to the feedback gain matrix K determined in III step, with unsteadiness of wheels speed and displacement z ₁, body vibrations speed and displacement z ₂with pavement displacement q as state variable, determine Active suspension LQG control U _aexpression formula, that is:

$U_a=-K{\left[\begin{array}{ccccc}{\stackrel{\·}{z}}_2& {\stackrel{\·}{z}}_1& z_2& z_1& q\end{array}\right]}^T;$

Wherein, ${\left[\begin{array}{ccccc}{\stackrel{\·}{z}}_2& {\stackrel{\·}{z}}_1& z_2& z_1& q\end{array}\right]}^T$ For matrix $\left[\begin{array}{ccccc}{\stackrel{\·}{z}}_2& {\stackrel{\·}{z}}_1& z_2& z_1& q\end{array}\right]$ Transposed matrix;

(5) optimal design of ride comfort weighting coefficient:

1. ride comfort weighting coefficient optimal design realistic model is built

According to the 1/4 vehicle ride differential equation set up in step (1), and the control U that in step (4), IV step is tried to achieve _a, utilize Matlab/Simulink simulation software, build ride comfort weighting coefficient optimal design Simulink realistic model;

2. ride comfort weighting coefficient optimal design objective function is set up

According to the ride comfort weighting coefficient optimal design Simulink realistic model set up in 1. step, with ride comfort weighting coefficient α ₁, α ₂, α ₃for design variable, using road roughness displacement as input stimulus, vehicle ride situation is emulated, utilize the vehicle body Vertical Acceleration root-mean-square value emulating and obtain set up ride comfort weighting coefficient optimal design objective function J _o(α ₁, α ₂, α ₃), that is:

$J_o({\mathrm{\α}}_1,{\mathrm{\α}}_2,{\mathrm{\α}}_3)={\mathrm{\σ}}_{{\stackrel{\·\·}{z}}_2};$

3. ride comfort weighting coefficient Constrained Conditions in Optimal Design is set up

According to vehicle single-wheel unsprung mass m ₁, sprung mass m ₂, tire stiffness K _t, gravity acceleration g, and bump clearance of suspension [f _d], utilize tire vertical deviation z ₁, vehicle body vertical deviation z ₂, road roughness displacement q, and ride comfort weighting coefficient α ₁, α ₂, α ₃, set up ride comfort weighting coefficient Constrained Conditions in Optimal Design, namely

$\{\begin{array}{c}|z_1-q|\≤\frac{(m_1+m_2)g}{K_t}\\ |z_2-z_1|\≤\[f_d\]\\ 0\≤{\mathrm{\α}}_1\≤1\\ 0\≤{\mathrm{\α}}_2\≤1\\ 0\≤{\mathrm{\α}}_3\≤1\\ {\mathrm{\α}}_1+{\mathrm{\α}}_2+{\mathrm{\α}}_3=1\end{array};$

4. the optimal design of ride comfort weighting coefficient

According to the ride comfort weighting coefficient optimal design Simulink realistic model set up in 1. step, and the ride comfort weighting coefficient Constrained Conditions in Optimal Design 3. set up in step, with ride comfort weighting coefficient α ₁, α ₂, α ₃for design variable, using road roughness displacement as input stimulus, utilize optimized algorithm ask 2. in step institute set up ride comfort weighting coefficient optimal design objective function J _o(α ₁, α ₂, α ₃) minimum value, corresponding design variable is the optimum optimization design load of ride comfort weighting coefficient, i.e. α _1o, α _2o, α _3o;

(6) LQG Controller of Active Suspension Optimal Control Force U _aodesign:

I step: according to the 4. ride comfort weighting coefficient α that obtains of optimization order design in step (5) _1o, α _2o, α _3o, and the weighting matrix expression formula Q (α determined in step (3) ₁, α ₂, α ₃), R (α ₁, α ₂, α ₃), N (α ₁, α ₂, α ₃), calculate weighting matrices Q (α _1o, α _2o, α _3o), R (α _1o, α _2o, α _3o), N (α _1o, α _2o, α _3o);

Ii step: according to the state matrix A determined in step (2) and gating matrix B, and the weighting matrices Q (α determined in i step _1o, α _2o, α _3o), R (α _1o, α _2o, α _3o), N (α _1o, α _2o, α _3o), utilize the LQR function in Matlab to calculate the optimum control feedback gain matrix K trying to achieve Active suspension LQG _o;

Iii step: according to the Optimal Feedback gain matrix K determined in ii step _o, with unsteadiness of wheels speed and displacement z ₁, body vibrations speed and displacement z ₂with pavement displacement q as state variable, determine the Optimal Control Force U of LQG Controller of Active Suspension _ao, that is:

$U_{ao}=-K_o{\left[\begin{array}{ccccc}{\stackrel{\·}{z}}_2& {\stackrel{\·}{z}}_1& z_2& z_1& q\end{array}\right]}^T.$